VCE General Maths Recursion and Financial Modelling 2017 Exam 1 Mini Test
VCAA General Maths Exam 1
This is the full VCE General Maths Exam with worked solutions. You can also try Mini-Tests, which are official VCAA exams split into short tests you can do anytime.
Number of marks: 8
Reading time: 3 minutes
Writing time: 18 minutes
Instructions
• Answer all questions in pencil on your Multiple-Choice Answer Sheet.
• Choose the response that is correct for the question.
• A correct answer scores 1; an incorrect answer scores 0.
• Marks will not be deducted for incorrect answers.
• No marks will be given if more than one answer is completed for any question.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.
Recursion and financial modelling - 2017
The first five terms of a sequence are 2, 6, 22, 86, 342 ...
The recurrence relation that generates this sequence could be
- A. \(P_0 = 2, \quad P_{n+1} = P_n + 4\)
- B. \(P_0 = 2, \quad P_{n+1} = 2P_n + 2\)
- C. \(P_0 = 2, \quad P_{n+1} = 3P_n\)
- D. \(P_0 = 2, \quad P_{n+1} = 4P_n - 2\)
- E. \(P_0 = 2, \quad P_{n+1} = 5P_n - 4\)
Use the following information to answer Questions 19 and 20.
Shirley would like to purchase a new home. She will establish a loan for $225 000 with interest charged at the rate of 3.6% per annum, compounding monthly.
Each month, Shirley will pay only the interest charged for that month.
After three years, the amount that Shirley will owe is
- A. $73 362
- B. $170 752
- C. $225 000
- D. $239 605
- E. $245 865
Let \(V_n\) be the value of Shirley's loan, in dollars, after \(n\) months.
A recurrence relation that models the value of \(V_n\) is
- A. \(V_0 = 225\,000, \quad V_{n+1} = 1.003\,V_n\)
- B. \(V_0 = 225\,000, \quad V_{n+1} = 1.036\,V_n\)
- C. \(V_0 = 225\,000, \quad V_{n+1} = 1.003\,V_n - 8100\)
- D. \(V_0 = 225\,000, \quad V_{n+1} = 1.003\,V_n - 675\)
- E. \(V_0 = 225\,000, \quad V_{n+1} = 1.036\,V_n - 675\)
A printer was purchased for $680.
After four years the printer has a value of $125.
On average, 1920 pages were printed every year during those four years.
The value of the printer was depreciated using a unit cost method of depreciation.
The depreciation in the value of the printer, per page printed, is closest to
- A. 3 cents.
- B. 4 cents.
- C. 5 cents.
- D. 6 cents.
- E. 7 cents.
Consider the graph below.
This graph could show the value of
- A. a piano depreciating at a flat rate of 6% per annum.
- B. a car depreciating with a reducing balance rate of 6% per annum.
- C. a compound interest investment earning interest at the rate of 6% per annum.
- D. a perpetuity earning interest at the rate of 6% per annum.
- E. an annuity investment with additional payments of 6% of the initial investment amount per annum.
Four lines of an amortisation table for an annuity investment are shown below.
The interest rate for this investment remains constant, but the payment value may vary.
| Payment number |
Payment | Interest | Principal addition |
Balance of investment |
|---|---|---|---|---|
| 17 | 100.00 | 27.40 | 127.40 | 6977.50 |
| 18 | 100.00 | 27.91 | 127.91 | 7105.41 |
| 19 | 100.00 | 28.42 | 128.42 | 7233.83 |
| 20 | 7500.00 |
The balance of the investment after payment number 20 is $7500.
The value of payment number 20 is closest to
- A. $29
- B. $100
- C. $135
- D. $237
- E. $295
Xavier borrowed $245 000 to pay for a house.
For the first 10 years of the loan, the interest rate was 4.35% per annum, compounding monthly.
Xavier made monthly repayments of $1800.
After 10 years, the interest rate changed.
If Xavier now makes monthly repayments of $2000, he could repay the loan in a further five years.
The new annual interest rate for Xavier’s loan is closest to
- A. 0.35%
- B. 4.1%
- C. 4.5%
- D. 4.8%
- E. 18.7%
End of Multiple-Choice Question Book
VCE is a registered trademark of the VCAA. The VCAA does not endorse or make any warranties regarding this study resource. Past VCE exams and related content can be accessed directly at www.vcaa.vic.edu.au
